Question: Simplify the following expression: $ k = \dfrac{4q - 1}{q - 4} + \dfrac{9}{7} $
Solution: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{7}{7}$ $ \dfrac{4q - 1}{q - 4} \times \dfrac{7}{7} = \dfrac{28q - 7}{7q - 28} $ Multiply the second expression by $\dfrac{q - 4}{q - 4}$ $ \dfrac{9}{7} \times \dfrac{q - 4}{q - 4} = \dfrac{9q - 36}{7q - 28} $ Therefore $ k = \dfrac{28q - 7}{7q - 28} + \dfrac{9q - 36}{7q - 28} $ Now the expressions have the same denominator we can simply add the numerators: $k = \dfrac{28q - 7 + 9q - 36}{7q - 28} $ $k = \dfrac{37q - 43}{7q - 28}$